It's true that gold and silver have industrial uses, but you don't see people hoarding bars of chromium as a store if value. I doubt that gold's price is entirely due to industrial demand...
Now I hand him a stack of papers with numbers printed on them. The goat breeder has no use for these papers, but he also had no use for the gold. He'd need to trade them for something. Let's run it all back up the same line and we see it doesn't end at "and now the smelter has something useful" because paper isn't useful to the smelter either... but running the paper through that chain of merchants has proven that there's value attached to the paper. The smelter then recognizes the value of the paper and trades the paper to the miners who supply the metal, because the traders who supply the metal want to buy some goat milk from me and they know I accept this weird paper in exchange for my goat's milk.
That's how currency has worked since the beginning of civilization. Ancient people weren't melting down coins to make something more valuable, they were trading the coins as-is without a worry about how useful the raw materials are. They just needed something anything that everyone agreed had a certain amount of value to it that's also difficult to fake. Gold has no intrinsic value for 90% of all humans on the planet, it's just a way to exchange goods and services based on an arbitrary-but-universally-recognized token.
I’d assume it’s more work to dig up and purify gold ore than make linen paper. Wouldn’t this mean some currencies are inherently more stable?
Gold and silver works great for newer and less technologically advanced civilizations, because it's easier to smelt metal than print new US Dollars on speciality linen paper. It would be easier to lose the ability to smelt metal and then later regain that ability than it is to lose the ability to print USD and try to regain it. But once you reach a certain level of technological sophistication, minting fake gold coins becomes easier than printing new USD and people start to trust the currency less.
So I guess yes, precious metals would be easier to rebuild civilization with because it could be more easily reproduced as technology advances. But no matter what I think every civilization would abandon precious metals as they progressed, because counterfeiting becomes very easy very quickly.
But you have to buy them. You can't buy things with them.
You might be able to barter, if you can find someone who has what you want, and also happens to need some 6 9's pure gallium indium phosphide or whatever.
However, the guy at the corner liquor store is unlikely to give you a bottle of whiskey in exchange for it.